Given the large size and complexity of most biochemical regulation and signaling networks, there is a non-trivial relationship between the micro-level logic of component interactions and the observed macro-dynamics. Here we address this issue by formalizing the existing concept of pathway modules, which are sequences of state updates that are guaranteed to occur (barring outside interference) in the dynamics of automata networks after the perturbation of a subset of driver nodes. We present a novel algorithm to automatically extract pathway modules from networks and we characterize the interactions that may take place between modules. This methodology uses only the causal logic of individual node variables (micro-dynamics) without the need to compute the dynamical landscape of the networks (macro-dynamics). Specifically, we identify complex modules, which maximize pathway length and require synergy between their components. This allows us to propose a new take on dynamical modularity that partitions complex networks into causal pathways of variables that are guaranteed to transition to specific states given a perturbation to a set of driver nodes. Thus, the same node variable can take part in distinct modules depending on the state it takes. Our measure of dynamical modularity of a network is then inversely proportional to the overlap among complex modules and maximal when complex modules are completely decouplable from one another in the network dynamics. We estimate dynamical modularity for several genetic regulatory networks, including the Drosophila melanogaster segment-polarity network. We discuss how identifying complex modules and the dynamical modularity portrait of networks explains the macro-dynamics of biological networks, such as uncovering the (more or less) decouplable building blocks of emergent computation (or collective behavior) in biochemical regulation and signaling.
翻译:鉴于大多数生化调控和信号传递网络的规模和复杂性,组件相互作用的微观逻辑与观察到的宏观动力学存在着非平凡的关系。在这里,我们通过形式化现有的通路模块概念来解决这个问题,通路模块是指在干扰子节点的子集后,保证在自动机网络的动态中(除非外界干扰),会发生的状态更新序列。我们提出了一种新算法来自动提取网络中的通路模块,并且我们对模块之间可能发生的相互作用进行了表征。此方法只使用单个节点变量的因果逻辑(微观动态),而不需要计算网络的动态景观(宏观动态)。具体而言,我们确定了复杂模块,这些模块最大化通路长度,并需要其组件之间的协同作用。这使我们能够提出一种新的动态模块方法,将复杂网络划分为因果变量路径,这些变量在给定驱动器节点集的干扰下保证转换到特定状态。因此,同一个节点变量可以根据其所取的状态参与不同的模块。我们的网络动态模块度量与复杂模块之间的重叠成反比,当复杂模块在网络动态中完全不相关时,达到最大值。我们估计了几个遗传调控网络的动态模块度,包括果蝇段极性网络。我们讨论了如何通过识别复杂模块和生物网络的动态模块度特征来解释生物网络的宏观动态,例如揭示生化调控和信号传递中新兴计算(或集体行为)的不同程度无关的构建块。